FIND SLOPE OF THE TANGENT TO THE CURVE AT THE POINT WORKSHEET

Use the first derivative to find the slope of the tangent line to the given curve at the given point:

Problem 1 :

y = 2x² + 6 at (-1, 8)

Problem 2 :

y = -x² + 2x - 3 at (2, 3)

Problem 3 :

y = 4 - 3x³ at (1, 1)

Problem 4 :

Problem 5 :

Tangent lines are drawn to the parabola

y = x² at (2, 4) and (-1/8, 1/64)

Prove the tangents are perpendicular.

Problem 6 :

Find a point on the parabola

y = -x² +3x + 4

where the slope of the tangent line is 5.

Problem 7 :

Find the slope of the tangent line to the graph of

3x² + 5 lny = 12 at (2, 1) is

A) -12/5 B) 12/5 C) 5/12 D) 12 E) -7

Problem 8 :

Answer Key

1) 2

2) 0

3) -5

4) 8

5) So, the tangents drawn at the points (2, 4) and (-1/8, 1/64) for the parabola, they are perpendicular.

6) the required point is (-1, 0).

7) the required slope is -12/5. Option A.

8) the required value of y is 58/7, option C.